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"`<M  0 FdL  0 # TIf  2 TA :-? ? ` 0 :- F  <F# X^  @C  F ` f   Q N ` P    ` f    <F  1x   <F&   1z2   BF3y" p@ < z2   <y" 0P rB B BD@rB B BD`ZB  s *DZB  s *D    nBC2DEFJh..h003C8o@DSXbchmhx 2 4@Wfox84 Xh(""$@               `"`B   nBC2DEFJ3R8..":RN038@DSXbchzmjhOxJE .46@RWfx0kX2h(" ""$@               `"`0B  <0F  1bfB  6Df  0fY"`'"XB  0Dm=  TTF ??" U kc(s): number of partons produced per participating nucleon in AA collision, which is a constant.DlA;AA)A$T*  T ??"zw  4Collective longitudinal momentum per produced parton&54AA.   T ??"Mm 5P 2 ! T  ??"3:S  5T 2B #  `D??" m If $ 0Y"`:#f % 0Y"`T#XB & 0Df7J& +0  `A; 0?  "`m  0 dH  0޽h ? ̙33___PPT10i.M0+D=' P= @B +  0 F>A B (   fF     >'  " XA#   geo3P  h   s *"`  B  3 rA ??#" `I  A  3 rA8 ??#" ` ~   s *@ wb   F P     n2   03E"`  T  kN   # P &/ fB  B 6DN N ZB   s *D N pN  kH     kH fB   6D k    0< FH  < n2   03q}"`PpZB  B s *DZB   s *Dp`n2   03E"`P z   <3f" `xX z   <3f" `ZB   s *DPX@ ZB  B s *Dx( ` .  c $A !?? V  ! 4 0 6A /?   / x 5  <A /?  G  /x 6  <A .? V m q  .x 7  <A" /?  m n0 / :  Tx ??"z  pfor Au+Au at 200AGeV 2C  ;  T# ??" `for Dx=1fm0  2C >  c $A! /? ?"` 6t  /$D 0dB @  Z??#" ` F ,$D 0H   0޽h ? ̙33zr___PPT10R.T +D&' P= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@ %(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*> %(+  0 . & P (    NA  ??"da }~  s * Q wb     c $W jP V >6___PPT9 :Scattering amplitude in momentum space obtained as usual: N: " dA&AA:x V { | 0 TA 0? ? zj  0  0 TA 0? ? TSn  0 `  c $A| 0?? 0`  c $Aw 0??]FFm 0`   c $A 0??M} 0`   c $A 0??Q 0   Tk ??"  IMake a two dimensional Fourier transformation to impact parameter space :J 2JA   <v S  OUn-polarized cross section:A  0 TA 0? ?   F  0   <c   HSpin dependent part:Af  s *A 0? ?Y   0f  s *A 0? ?M   0  T| ??"9 =Y [Quark polarization:, Af  s *A 0? ?9 0  0  Z ??"X  T ??"mg G reaction plan 2CH  0޽h ? ̙33___PPT10i.[pm!+D=' P= @B +  0  >d(  d 0d TO 3??#" `~  l&Scattering amplitude in momentum space*' 2AA  0? ?  'C_  0 `  d c $A| B-?? B-`  d c $Aw C-??]FFm C-`  d c $A D-??M} D-` d c $A E-??Q E- d 06l f  F un-polarized G& d0  `A O-? ? "`1   O- d d <Cp  7Differential cross section w.r.t. the impact parameter 88A d s *A 0? ?"` vFx 0d d TtN ??"I0 i [Quark polarization:, Af d s *A ^-? ? @  ^- /d TS ??"mg G reaction plan 2C2 3d Z ??#" ` 4d <p0 C Ispin dependenceGv 5d s *Aw 0??p  0 2 7d Z ??#" `   8d s *A= 0? ?"` a x 0d 9d s *A@ 0? ?"` pl x 0d" =d  `3s ??#" `   d Tx@??#" `<7~  Aa 2-dimensional Fourier transformation to impact parameter space "BPBGfH d 0޽h ? ̙33___PPT10i.[pm!+D=' P= @B +  0  V@(   V 3 r  b[A  ??#" `  P TA  ??#" `z ~  s *^ wb    v < s *A !??F  ! ` = c $A| !??^ !` > c $A !??/_ !` ? c $Aw !??mtt} !2 B Z??#" `+mr D Tx|??"\B E  `D)??"/ T T` ??"   talk by Gao Jian-hua 2A, U Z ??#" ` T H  0޽h ? ̙33___PPT10i.api+D=' P= @B +  0 `''x*(  xr x S i wb   r x S j <   F   x In2 x 03q}"`  ZB xB s *D @ 0ZB x s *D ` N   x  n2  x 03E"` T  x   x# `R  x 0f x `2  x 0̙ fb  x 6_ ` x 0u< T  x  x# ajn `R x 0f x `2 x 0̙ fb x 6_ ` x 0u< T  x  x# zir`R x 0f x `2 x 0̙ fb x 6_ ` x 0u< T  x  x# b Z`R x 0f x `2 x 0̙ fb x 6_ ` x 0u< T  x  x# n0{`R x 0f x `2  x 0̙ fb !x 6_ ` "x 0u< hF `I  #x  DN   $x `0( v %x c .A#  geo3P  h &x s *"`  'x <@v I RA New Picture of QGP in A+AC H x 0޽h ? 3333___PPT10i.Fh+D=' P= @B +'  0 &&P"G&(  x  c $Ѐ wb`   x  c $ j  !l ,  ~ #">y>'Z  +  `< ??"E , VNF___PPT9(   6(1+Ps2 )v (" dckkcC @` *  ` ??" E  VNF___PPT9(   3-4PqPs+Ps2 (" dckckckkC  @` )  `0 ??"E VNF___PPT9(   3-4PqPs+Pq2 (" dckckckkC  @` (  `D ??"E  VNF___PPT9(   3(1-P q2 )v (" dckkcC  @` '  `0 ??"E  VNF___PPT9(  RH 12(" dckccC  @` &  `X ??" ,E F>6___PPT9 2Ps(5+Ps2 )/ RW(" dckckkc  @`& %  ` ??" E F>6___PPT9 2$(4Ps-Pq-3Ps2 )/ RX(" dckckckkc  @`P $  `x ??" E F>6___PPT9 \((4Pq-Ps-3PsPq2 )/ RS(" dckckckckkc  @` #  ` ??" E VNF___PPT9(  PsP(" dckC  @` "  ` ??" E VNF___PPT9(  PHP(" dckC  @`| !  ` ??", F>6___PPT9 W.(" d   @`|    `4 ??"  F>6___PPT9 X.(" d   @`|   `) ??" F>6___PPT9 S.(" d   @`|   `0 ??" F>6___PPT9 L.(" d   @`   `h; ??" VNF___PPT9(  Hyperon<(" dcC @`B , T1 ??",B - T1 ??" , B . T1 ??" B / T1 ??",, B 2 T1 ??" , B 4 T1 ??" B 7 T1 ??" B : T1 ??"  B = T1 ??" B A T1 ??"E ,E  { T@ ??"'2 @Assuming  2 Af | s *A_ +? ? j + } 0A /?̙ ?"` x /dv  s *A% /? ? 9  /   TE ??" G9  =If  2C H  0޽h ? 3333___PPT10i.:?+D=' P= @B +  0  f(  x  c $ wb   x  c $5 jq     T ??" SIn analogue to & 2A 0 NA +? ? m r +    `A ??" kT   Tt ??#"  `S @ m  Theoretical results by assuming: Only L s containing the initial quark are polarized. Polarization of L is calculated using SU(6) wave-function.r! p l&A?*   Tb ??#" `pw iBoros, Liang, PRD(98) 2CB    fDo??" t H  0޽h ? 3333___PPT10i.U;+D=' P= @B +.  0 --1s~-(  ~  s *g4 wb  4 ~  s *h4 / 4 &   p #""Peee  4` Z  `l4 ??"C F>6___PPT9 l0(" d  @`` X  `{4 ??"pC F>6___PPT9 l0(" d  @`` V  `؄4 ??" Cp F>6___PPT9 l0(" d  @`Z T  `4 ??"JC F>6___PPT9 f*(" dC  @`2 R  `4 ??"CJ f^V___PPT980 PH in the case of Pq =Ps(" dckCckck  @`` @  `4 ??"CF>6___PPT9 l0(" d  @`` >  ``4 ??"pCF>6___PPT9 l0(" d  @`` <  `D4 ??" pCF>6___PPT9 l0(" d  @`Z :  `4 ??"J CF>6___PPT9 f*(" dC  @`| 8  `@4 ??"JCF>6___PPT9 PH@(" dck  @``   `$4 ??"  F>6___PPT9 l0(" d  @``   `4 ??"p  F>6___PPT9 l0(" d  @``   `4 ??" p F>6___PPT9 l0(" d  @`Z   `44 ??"J F>6___PPT9 f*(" dC  @`   ` 8 ??" J f^V___PPT980 %PH in the case of Pq =Ps and ns =fs&(" dckCckckckckc $,  @`|   `P8 ??"F>6___PPT9 W.(" d   @`|   `8 ??"pF>6___PPT9 X.(" d   @`|   `*8 ??" pF>6___PPT9 S.(" d   @`|   `-8 ??"J F>6___PPT9 L.(" d   @`   `D>8 ??"JVNF___PPT9(  Hyperon<(" dcC @`B  T1 ??"B  T1 ??"  B  T1 ??" B   T1 ??" B ! T1 ??"B " T1 ??"JJ B # T1 ??"  B $ T1 ??"pp B % T1 ??" B 9 N1 ??"CCB S N1 ??"   +0 NA 9? ? } 9 8f 4 s *Aa <? ?}u ' <f 5 s *Ab ?? ?}' ?f 6 s *Ad B? ?w% Bf K s *Af P? ?z i  Pf L s *Ae N? ?g i  Nf M s *Ag K? ?)i  Kf N s *Ad L? ?wF  Lf c s *A$ /? ?@ p  /` d c $Ay ?? T  ` e c $Az ??T f q s *A$ /? ?F m B  /f r s *A$ /? ?F   /f s s *A$ /? ?*   /H  0޽h ? 3333___PPT10i.U;+D=' P= @B +  0  (  x  c $8w wb   x  c $x ]  '  TN ??"TX  The same for hyperons and anti-hyperons. (Approximately) the same for different hyperons. No polarization at b=0, increases approximately linearly with b. Finite for hyperons at small finite pT and y, increases with pT, eventually drops to zero at very high pT. n2mCC(CC&CCKCCCCK(CCKC>( VV& 0  `Aq ? ? "`     dH  0޽h ? 3333___PPT10i.Y;r+D=' P= @B +$  0 ;30(    Z??#" `  ~  s * wb   ~  s *D s,   0 TA' b/? ? @d  b/   T ??"' xHyperon: Spin self-analyzing parity violating decay HB+M.J= 26AA6 0 TA* c/? ? d` j  c/   T\ ??"P' p JVector meson: Strong decay VM1+M2.& 2AAf   s *A. d/? ? M > d/   Zz ??#" ` T  LSpin density matrix: 2AB   ZD??"F F    T ??"9VY 4jr00: probability for m=0; r00=1/3 for unpolarized V.6 2$& B    `D??"P B   `D??"  B @  `D??"  2   `??#" `9C`  c $A/ e/??7P e/`  c $A1 f/?? f/`  c $A5 g/??%   g/2  3 rcG6YH@I ??#" `W9`  c $A7 h/??   h/  # l ??#" ` c<  L rest frame of H/V 2A  T ??"+V%  ;H/V 2   `d ??#" `<} bB / M1@ 2CKCH  0޽h ? 3333___PPT10i.Z;m}+D=' P= @B +   0   З/ (    Z??#" `V x  c $4 wT   & 0  `A *? ? "`w * d& 0  `A  ? ? "`w&}  4d  0 NA, u ? ? $ u 4f  s *A0 } ? ?CP } f  s *A-  ? ?9 cP  `  c $AC ??y `  c $A9  ??Z   `  c $A (??% c  (  0A<  ? ?"`Hx  d  0A  ? ?"` P x  dA  T ??" Y!Taking y as the quantization axis" 2"AH  0޽h ? 3333___PPT10i.;`/+D=' P= @B +R  0 ia  |(  | | Z??#" ` Y~ | s * wP    |0  fA .? ? "`w .  |0  fA .? ? "`* . , |0  fA .? ? "`7 '< . d |0 TA .? ?  . f | s *A .? ?  .  | TZ ??"  UIn analogue to * 2Cf  | s *A .? ?- .f  | s *A( !/? ?  !/H | 0޽h ? 3333___PPT10i.;`/+D=' P= @B +  0 0 p(  px p c $ wb    p c $X jT@   &xSx y p NA) ??"<P  p NA3 ??"]  p NA4 ??"  p T ??" I GNucl-ex/0608034 2A p T ??"2 R GNucl-ex/0510069 2A  p T@ ??"  GNucl-ex/0605035 2AH p 0޽h ? 3333___PPT10i.qG.+D=' P= @B +E  0 \Tpl(  lr l S 85 wb  5 r l S 5  5  l TH5 ??" 'F  .<CHEN Jinhui from SINAP, DONG Xin from USTC: talks at Weihai, July 2006. CHEN Jinhui from SINAP, plenary talk at QM2006. TANG Zebo: talk at Xi An in November. HHWC C t*  H l 0޽h ? 3333___PPT10i.qG.+D=' P= @B +  0 P0(  x  c $5 wb  5 x  c $5 v 5 H  0޽h ? 3333___PPT10i.0H"+D=' P= @B +  0 @ ,b(  ,~ , s *h*5    5  ,  B@+5 "` 5 H , 0޽h ? 3333y___PPT10Y+D=' P= @B +N   0 .q(  x  c $l:5 wb  5   S @5 (  5 *@ABC!  T`G5 ??" &Y,$ 0 [Thank you for your attention!" 2G 6H  0޽h ? 3333 ___PPT10.>p+ϐ(D' H5= @B DD' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+8+0+0 +z 0 h(  hd h c $lP   5 h s *TZFl 09  5 tFQuantization direction could be different for initial and final states@H h 0e ? ̙3380___PPT10.`X 0 0^(  d  c $lN   5  s *d5l %%  5 ^Now I will discuss the event anisotropy. The idea behind the measurement is the following: For non-central collisions, as shown here, the overlapped region looks like a ellipsoid. Sometimes this is called elliptical flow. 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There exists a huge orbital angular momentum of the colliding system w.r.t. the reaction plan. Quarks and anti-quarks are polarized in the opposite direction as the reaction plan due to spin-orbital interaction in QCD. Many consequences, many open questions & & 0n#7GGPGGOOGGOG)GVOutlook( & & & & & & & & & A possible method to study the role of orbital angular momentum in high energy spin physics. An effective way to study spin-orbital interaction in QCD? 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F8j2$q'Aؚirtf[Ot^O 02006t^10g28-11g1e Bhg0 Zh\OX(Liang Zuo-tang) q\N'Yf[(Shandong University)O =.ؚirtf[O,{NJ\hQVOXTNh'YOff[/gt^O (Z EGlobally polarized QGP in non-central AA collisions at high energies(FZF$ Introduction*  (LDo spin physics in AA collisions such as at RHIC without beam polarization?!>M0n1AEA0Elliptic flow and reaction plane in AA collisionZ1$GG GG v Global Orbital Angular Momentum &!F @ oGlobal orbital angular momentum G(.Gradients in pz-distribution along x-directionR/0Z C C K C   w%Transverse Gradient of Shear Velocity&&F Local Orbital Angular MomentumG(*Quark Scattering with fixed reaction plane4+*G$O$Quark PolarizationE(  #Consequence I: Hyperon polarization$$G$PRecombination mechanism (q1q2q3)H :)EGOGOGOGG#Consequence I: Hyperon polarization$$G$FFragmentation mechanism q H + X.n$EE#Consequence I: Hyperon polarization$$G$HFragmentation mechanism q H + X.%EAEE#Consequence I: Hyperon polarization$$G$Some of the expected featuresC +Consequence II: Vector meson spin alignment,,G 7No need to determine the direction of the reaction plan88E: Recombination mechanism2G(G$ : Fragmentation mechanism2G(G$"Experiments: Hyperon polarization $#!C$( ;Ilya Selyuzhenkov from Wayne State Univ. for STAR at RHIC<<A$ +)Experiments: Vector meson spin alignment $*(C$(China-STAR group:" 2G0Still many open questions(More realistic calculations taking flow into account; (Gao Jian-hua s talk) Influence from final state interaction; Influence of orbital angular momenta in hadronization; Relation to hyperon polarization w.r.t. production plan; Other measurable consequences; & & & D7 2 2 2 CAt< M 7XxSummaryG(2A great advantage to study spin effects in non-central AA-collisions is: the reaction plan can be determined experimentally by measuring v1 and v2. 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F8j2$q'Aؚirtf[Ot^O 02006t^10g28-11g1e Bhg0 Zh\OX(Liang Zuo-tang) q\N'Yf[(Shandong University)O =.ؚirtf[O,{NJ\hQVOXTNh'YOff[/gt^O (Z EGlobally polarized QGP in non-central AA collisions at high energies(FZF$ Introduction*  (LDo spin physics in AA collisions such as at RHIC without beam polarization?!ZM0nAAAEA0Elliptic flow and reaction plane in AA collisionZ1$GG GG v Global Orbital Angular Momentum &!F @ oGlobal orbital angular momentum G(.Gradients in pz-distribution along x-directionR/0Z C C K C   w%Transverse Gradient of Shear Velocity&&F Local Orbital Angular MomentumG(*Quark Scattering with fixed reaction plane4+*G$O$Quark PolarizationE(  #Consequence I: Hyperon polarization$$G$PRecombination mechanism (q1q2q3)H :)EGOGOGOGG#Consequence I: Hyperon polarization$$G$FFragmentation mechanism q H + X.n$EE#Consequence I: Hyperon polarization$$G$HFragmentation mechanism q H + X.%EAEE#Consequence I: Hyperon polarization$$G$Some of the expected featuresC +Consequence II: Vector meson spin alignment,,G 7No need to determine the direction of the reaction plan88E: Recombination mechanism2G(G$ : Fragmentation mechanism2G(G$"Experiments: Hyperon polarization $#!C$( ;Ilya Selyuzhenkov from Wayne State Univ. for STAR at RHIC<<A$ +)Experiments: Vector meson spin alignment $*(C$(China-STAR group:" 2G0Still many open questions(More realistic calculations taking flow into account; (Gao Jian-hua s talk) Influence from final state interaction; Influence of orbital angular momenta in hadronization; Relation to hyperon polarization w.r.t. production plan; Other measurable consequences; & & & D7 2 2 2 CAt< M 7XxSummaryG(2A great advantage to study spin effects in non-central AA-collisions is: the reaction plan can be determined experimentally by measuring v1 and v2. 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F8j2$q'Aؚirtf[Ot^O 02006t^10g28-11g1e Bhg0 Zh\OX(Liang Zuo-tang) q\N'Yf[(Shandong University)O =.ؚirtf[O,{NJ\hQVOXTNh'YOff[/gt^O (Z EGlobally polarized QGP in non-central AA collisions at high energies(FZF$ Introduction*  (LDo spin physics in AA collisions such as at RHIC without beam polarization?!ZM0nAAAEA0Elliptic flow and reaction plane in AA collisionZ1$GG GG v Global Orbital Angular Momentum &!F @ oGlobal orbital angular momentum G(.Gradients in pz-distribution along x-directionR/0Z C C K C   w%Transverse Gradient of Shear Velocity&&F Local Orbital Angular MomentumG(*Quark Scattering with fixed reaction plane4+*G$O$Quark PolarizationE(  #Consequence I: Hyperon polarization$$G$PRecombination mechanism (q1q2q3)H :)EGOGOGOGG#Consequence I: Hyperon polarization$$G$FFragmentation mechanism q H + X.n$EE#Consequence I: Hyperon polarization$$G$HFragmentation mechanism q H + X.%EAEE#Consequence I: Hyperon polarization$$G$Some of the expected featuresC +Consequence II: Vector meson spin alignment,,G 7No need to determine the direction of the reaction plan88E: Recombination mechanism2G(G$ : Fragmentation mechanism2G(G$"Experiments: Hyperon polarization $#!C$( ;Ilya Selyuzhenkov from Wayne State Univ. for STAR at RHIC<<A$ +)Experiments: Vector meson spin alignment $*(C$(China-STAR group:" 2G0Still many open questions(More realistic calculations taking flow into account; (Gao Jian-hua s talk) Influence from final state interaction; Influence of orbital angular momenta in hadronization; Relation to hyperon polarization w.r.t. production plan; Other measurable consequences; & & & D7 2 2 2 CAt< M 7XxSummaryG(2A great advantage to study spin effects in non-central AA-collisions is: the reaction plan can be determined experimentally by measuring v1 and v2. 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F8j2$q'Aؚirtf[Ot^O 02006t^10g28-11g1e Bhg0 Zh\OX(Liang Zuo-tang) q\N'Yf[(Shandong University)O =.ؚirtf[O,{NJ\hQVOXTNh'YOff[/gt^O (Z EGlobally polarized QGP in non-central AA collisions at high energies(FZF$ Introduction*  (LDo spin physics in AA collisions such as at RHIC without beam polarization?!ZM0nAAAEA0Elliptic flow and reaction plane in AA collisionZ1$GG GG v Global Orbital Angular Momentum &!F @ oGlobal orbital angular momentum G(.Gradients in pz-distribution along x-directionR/0Z C C K C   w%Transverse Gradient of Shear Velocity&&F Local Orbital Angular MomentumG(*Quark Scattering with fixed reaction plane4+*G$O$Quark PolarizationE(  #Consequence I: Hyperon polarization$$G$PRecombination mechanism (q1q2q3)H :)EGOGOGOGG#Consequence I: Hyperon polarization$$G$FFragmentation mechanism q H + X.n$EE#Consequence I: Hyperon polarization$$G$HFragmentation mechanism q H + X.%EAEE#Consequence I: Hyperon polarization$$G$Some of the expected featuresC +Consequence II: Vector meson spin alignment,,G 7No need to determine the direction of the reaction plan88E: Recombination mechanism2G(G$ : Fragmentation mechanism2G(G$"Experiments: Hyperon polarization $#!C$( ;Ilya Selyuzhenkov from Wayne State Univ. for STAR at RHIC<<A$ +)Experiments: Vector meson spin alignment $*(C$(China-STAR group:" 2G0Still many open questions(More realistic calculations taking flow into account; (Gao Jian-hua s talk) Influence from final state interaction; Influence of orbital angular momenta in hadronization; Relation to hyperon polarization w.r.t. production plan; Other measurable consequences; & & & D7 2 2 2 CAt< M 7XxSummaryG(2A great advantage to study spin effects in non-central AA-collisions is: the reaction plan can be determined experimentally by measuring v1 and v2. 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